1. Three-Dimensional Representation of Motor Space in the Mouse Superior Colliculus 
Jonathan J. Wilson, Nicolas Alexandre, Caterina Trentin, Marco Tripodi 
Current Biology 
Volume 28, Issue 11, Pages e12 (June 2018)
DOI: /j.cub
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2. Current Biology 2018 28, 1744-1755.e12DOI: (10.1016/j.cub.2018.04.021)
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3. Figure 1
Inertial Sensor-Based Approach to Monitor 3D Head Displacements
(A) Cartoon depicting the three Eulerian axes about which head rotations can occur, showing the yaw axis (magenta), pitch axis (cyan), and roll axis (orange). Curved arrows show the definition of rotation directions about each axis. (Right) Separate examples of a clockwise yaw, downward pitch, and counter-clockwise roll rotation relative to an axis-aligned starting position are shown.
(B) Cartoon of the inertial sensor and flow schematic showing the implementation of the direction cosine matrix algorithm with the sensor. Gyroscopic information for the three axes is passed through a rotation matrix to determine the orientation of heading. Inputs from accelerometer and magnetometer chips detect drift in the gyroscopic signal before the error is calculated and adjusted for.
(C) Box and whisker plots showing the jitter in the sensor system in static regime for each sample recorded at 50 Hz.
(D) Line plots depicting the total cumulative drift in the system over 20 min.
(E) Line plots showing the sensor output during rotations of the sensor over 360° at four different speeds and two directions (colored lines) and the expected measurement (black dashed line).
(F) Bar chart showing the error for each sample at each speed (lighter shades show clockwise rotations; dark shades for counter-clockwise rotations), depicted as mean ± SEM. The error is measured in degrees for each expected degree per temporal bin.
(G) Implementation of the sensor aligned with tetrode recordings showing the traces of yaw (magenta), pitch (cyan), and roll (orange) aligned to the bursting activity of a neuron recorded from the SC (black lines represent spikes; highlighted gray area indicates the bursting window).
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4. Figure 2
Angular Head Displacements Are Relatively Unconstrained in Mice
(A–E) One-dimensional kinematics of head motion.
(A) Cartoon depicts examples of rotations around each of the three Eulerian axes.
(B) Histograms showing the sampling of movements for each of the axes (yaw, magenta; pitch, cyan; roll, orange) from the trials of one animal. Dashed line shows the Gaussian curve fitted to the histogram of sampled movements.
(C) Line plots showing the animal averages (solid lines; n = 9) and population average (black dashed line) of the Gaussian curves fitted to the movement sampling data in yaw (magenta), pitch (cyan), and roll (orange).
(D and E) Bar charts showing the mean ± SEM of the center (D) and SD (E) of fitted Gaussian curves from the analyses of nine mice over 96 recording trials.
(F) Cartoons showing examples of the three possible pairings of conjunctive head motion. Left to right: yaw × pitch, yaw × roll, and pitch × roll motions are shown.
(G) Heatmaps depicting the sampling of head motions for each pair of conjunctive motions taken from the trials (n = 8) of one mouse. Warmer colors represent greater sampling. Black dashed lines depict the output of the regression carried out for this mouse.
(H and I) Scatterplots showing the individual regression coefficient (H) and associated R2 values (I) for each mouse (n = 9) in each pair of conjunctive motions. The mean ± SEM of the mice is shown to the left of each group of scatterplots in black.
(J) Quaternion representation of conjunctive motion sampling from the mouse shown in (G).
(K) Torsional SD values taken from the 1st and 2nd order fitting of Listing’s planes and Fick’s plane (bars) compared to previous studies in primates (red dashed line). Data depicted as mean ± SEM.
See also Tables S1 and S2.
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5. Figure 3 Tuning of Collicular Neurons to 3D Head Rotations
(A) Cartoon depicting the attachment of the sensor to the recording system. The sensor was attached to the side of the headstage, which was connected to the implanted microdrive for recording sessions.
(B) Example histology showing the photomicrograph of a thionine-stained section (left) and the estimated position taken from the mouse brain atlas [29]. Red dot shows the estimated final position of the tetrodes in the intermediate SC.
(C–F) Examples of burst-triggered average analyses (BTA) showing neurons decoding contralateral yaw only (C), downward pitch only (D), counter-clockwise roll only (E), and conjunctive 3D rotations around all three axes—CW yaw, upward pitch, and CCW roll (F). Cartoons on the left depict the resulting motion of the head from each of these neurons, from an axis-aligned starting position. Colored line plots show the burst-triggered average displacements 0.5 s before and 1 s after the onset of bursting for yaw (magenta), pitch (cyan), and roll (orange). Quasi-horizontal black lines depict the mean of displacement angles drawn from shuffled data at each time point. Vertical black lines depict burst onset. Bold colored line depicts mean displacement angle at each time point, and shaded areas depict SEM.
(G–I) Comparisons of the resultant motion for cells with yaw tuning (n = 18; G), pitch tuning (n = 17; H), and roll tuning (n = 6; I) for each of the light trials. Note the consistency of tuning across trials.
(J) Venn diagram depicting the percentage of motion-tuned cells (n = 32) that are tuned to yaw, pitch, roll, or are conjunctively tuned to yaw and pitch, yaw and roll, or yaw, pitch, and roll.
See also Figures S1, S2, S3, and S4.
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6. Figure 4
Firing Rate Is Modulated by Angular Velocity, but Not Displacement Angle
(A–D) Burst rate and duration are not related to tuning.
(A) Scatterplot showing an example of the relation between firing rate and displacement angle for one yaw-tuned cell. Black line shows fit regression line.
(B) Scatterplot showing the mean ± SEM of the slope and R2 values of the regressions carried out between burst rate and displacement angles for motion-tuned neurons with yaw (n = 18), pitch (n = 17), or roll (n = 6). Note the low R2 values.
(C) Scatterplot showing the relationship between burst duration and displacement angle for one yaw-tuned cell.
(D) Scatterplot showing the mean ± SEM of R2 values and regression coefficients for the regression carried out between burst duration and displacement angles for motion-tuned neurons with yaw (n = 18), pitch (n = 17), or roll (n = 6).
(E–H) Velocity tuning of four representative cells tuned to (E) yaw, (F) pitch, (G) yaw and pitch, and (H) yaw and roll. (Left plots) Burst-triggered average plots for neurons display the mean ± SEM displacement in the 0.5 s prior to and 1.0 s after bursting onset (vertical line), only shown for the component in which burst-triggered average analyses revealed motion tuning. Horizontal lines show the mean of the shuffled distribution for the cell. (Right) Line plots for the same cells show the increase in firing rate with angular head velocity for the component in which cells are tuned. Grey lines show the results of model fitting for the constant model (dashed line) and skewed Gaussian model (solid line).
See also Figure S5.
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7. Figure 5 Light-Independent Tuning of SC Neurons
(A) Line plots showing burst-triggered averages of head displacements for neurons decoding yaw (left), pitch (middle), or roll (right) in light trials (top) and dark trials (bottom). Note the similarity of tuning between light and dark trials.
(B) Comparisons of the mean displacement angles in light and dark trials. Note that not all neurons maintain tuning in dark conditions.
(C) Bar (mean ± SEM) and scatterplots depicting the absolute displacement angle of neurons in light trials (light shaded bars) and dark trials (darker shaded bars). For clarity, only neurons that maintained the same direction of tuning in light and dark trials are shown in (C).
(D) Gaussian curves were fit to the sampling frequencies of head displacement events for dark trials (darker shades) as well as light trials (lighter shades, also shown in Figures 2D and 2E) for each of the three Eulerian axes. There was no effect of condition (light versus dark) on the mean of the fit Gaussian curves.
(E) There was an effect of condition on the SD of the fit Gaussian curve, as well as an interaction between Eulerian component and condition, shown by an increased range of sampling in the yaw and roll axes in dark conditions.
(F and G) The results of regression analyses for conjunctive movements in light (lighter shades) and dark (darker shades) for each pair of conjunctive movements. There was no effect of condition on either the associated R2 values (F) or regression coefficient (G) for any of the conjunctive pairings.
In (D)–(G), motion sampling in darkness depicted as mean ± SEM.
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8. Figure 6 Motion Tuning Is Independent of Landmark Cues
(A) BTA plots of a motion-tuned cell with a preference for clockwise yaw shown at six azimuthal headings (60° bins). Polar plot shows the dwell-time-normalized number of bursts in each bin. Line plots show the BTAs of the cell at each of these headings. Note the similarity in tuning.
(B) Scatterplots showing the difference in tuning between recording trials and shuffled distributions for azimuth (left), elevation (middle), and bank (right) for each light trial. Data are shown for all motion-tuned cells (n = 32). For azimuth tuning, Rayleigh vector scores were compared—cells with consistently higher Rayleigh scores than 95% of the shuffled distribution (gray box) and a consistent preferred firing direction (within 30°) were considered to be modulated by azimuth heading (pink dots show tuned cells). Tuning width was compared for elevation and bank—only cells with tuning widths less than 5% of the shuffled distribution in both light trials (gray box) were considered to be modulated by elevation or bank heading. None of the motion-tuned cells were modulated by elevation or bank.
(C) Polar plots of a non-azimuth-modulated cell (top) and an azimuth-modulated cell (bottom) for both light trials.
(D) Examples of the lack of modulation in pitch (top) and roll (bottom) of one cell for both light trial 1 (left) and light trial 2 (right).
See also Figure S6.
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